Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer1879 |
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Resultat 1-5 av 13
Side 4
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . [ A radius is a straight line drawn from the centre to the circumference , and is therefore half the diameter . ] 18. A ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . [ A radius is a straight line drawn from the centre to the circumference , and is therefore half the diameter . ] 18. A ...
Side 7
... diameter ( or diagonal ) of a parallelogram is the straight line joining two of its opposite angles . [ At the close of the definitions Euclid inserts three Pos- tulates , that is , three things which he asks to be allowed to do ( from ...
... diameter ( or diagonal ) of a parallelogram is the straight line joining two of its opposite angles . [ At the close of the definitions Euclid inserts three Pos- tulates , that is , three things which he asks to be allowed to do ( from ...
Side 67
... diameter bisects them , that is , divides them into two equal parts . Let ACDB be a Then must AB = = A BCD . of which BC is a diameter . CD ; AC BD ; and △ ABC = A B Dem . AB is || CD , and BC meets them , .. ≤ ABC = △ BCD . and AC ...
... diameter bisects them , that is , divides them into two equal parts . Let ACDB be a Then must AB = = A BCD . of which BC is a diameter . CD ; AC BD ; and △ ABC = A B Dem . AB is || CD , and BC meets them , .. ≤ ABC = △ BCD . and AC ...
Side 68
... diameter bisects it . Q. E. D. [ Avoid two common errors : ( 1 ) when applying prop . 26 do not say ' therefore the triangles are equal in all respects ; ' ( 2 ) do not stop short after proving that the opposite sides and angles are ...
... diameter bisects it . Q. E. D. [ Avoid two common errors : ( 1 ) when applying prop . 26 do not say ' therefore the triangles are equal in all respects ; ' ( 2 ) do not stop short after proving that the opposite sides and angles are ...
Side 74
... diameter AB bisects GBCA , ( i . 34 ) .. △ ABC is half GBCA ; .. A DEF is half also , the diameter DF bisects DEFH , ( i . 34 ) but the halves of equal things are equal ; ( ax . 7 ) DEFH ; • AABC = ADEF . Therefore , triangles , & c ...
... diameter AB bisects GBCA , ( i . 34 ) .. △ ABC is half GBCA ; .. A DEF is half also , the diameter DF bisects DEFH , ( i . 34 ) but the halves of equal things are equal ; ( ax . 7 ) DEFH ; • AABC = ADEF . Therefore , triangles , & c ...
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Euclid, Books I. & II., with Notes, Examples, and Explanations, by a Late ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD algebraical angle equal base BC bisect Book called centre cloth coincide common Constr demonstration describe diagonal diameter difference divided double of sq double sq draw Edition equal equilateral triangle Euclid exterior angle extremity fall figure follows formed four geometrical given line given point given st given straight line gnomon greater half hypothesis isosceles triangle join length less Let ABC meet namely opposite sides parallel parallelogram perpendicular PROBLEM produced prop PROPOSITION proved rect rectangle contained remainder respects right angles shown square STANDARD THEOREM things third triangle twice twice rect unequal units vertex whole
Populære avsnitt
Side 48 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 32 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle. 17. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 109 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.
Side 1 - ... angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which \ is less than a right angle. 13. A term or boundary is the extremity of any thing.
Side 6 - Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Side 77 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 3 - An equilateral triangle is that which has three equal sides : 25. An isosceles triangle is that which has two sides equal : 26. A scalene triangle is that which has three unequal sides : 27.
Side 1 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Side 84 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.